Emergent Vorticity and Viscous Stress in Coarse-Grained Quantum Hydrodynamics

Quantum fluids are typically described by irrotational flow fields, with vorticity confined to singularities such as quantized vortices. In this talk, I present a coarse-graining framework for quantum hydrodynamics based on finite scale theory, which reveals the emergence of finite vorticity and viscous-like stress terms in the macroscopic equations of motion. Starting from the Madelung formulation of the nonlinear Schrödinger equation, I derive effective fluid equations where the Favre-averaged velocity field can support continuous vorticity and obeys a vorticity evolution equation analogous to that in classical fluids, including a vortex-stretching term. The resulting stress terms resemble artificial viscosity in computational fluid dynamics and suggest a natural scale at which quantum fluids exhibit quasi-classical behavior. I illustrate these results with an analytically tractable example of a coarse-grained line vortex, demonstrating how singular microscopic flows give rise to smooth, finite vorticity distributions. These findings offer a new perspective on the connection between quantum and classical turbulence and provide a potential bridge toward unified models of turbulent behavior across scales.